Structure of nonlinear gauge transformations

Details Structure of nonlinear gauge transformations Structure of nonlinear gauge transformations

1997-11-22

arxiv.org/abs/quant-ph/9711053v2

Phys.Rev. A57 (1998) 2263

Physics

Quantum Physics

Final version, to be published in Phys.Rev.A (Rapid Communication), April 1998

Scientific paper

10.1103/PhysRevA.57.R2263

Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations (NGT) defined in terms of a wave function $\psi(x)$ do not form a group. To get a group property one has to consider transformations that act differently on different branches of the complex argument function and the knowledge of the value of $\psi(x)$ is not sufficient for a well defined NGT. NGT that are well defined in terms of $\psi(x)$ form a semigroup parametrized by a real number $\gamma$ and a nonzero $\lambda$ which is either an integer or $-1\leq \lambda\leq 1$. An extension of NGT to projectors and general density matrices leads to NGT with complex $\gamma$. Both linearity of evolution and Hermiticity of density matrices are gauge dependent properties.

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